This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A339184 #6 Dec 07 2020 01:37:13
%S A339184 0,0,1,0,0,1,1,1,1,0,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,2,2,2,2,2,2,2,1,
%T A339184 1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,
%U A339184 3,3,3,3,3,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3
%N A339184 Number of partitions of n into two parts such that the larger part is a nonzero square.
%H A339184 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A339184 a(n) = Sum_{i=1..floor(n/2)} c(n-i), where c is the square characteristic (A010052).
%F A339184 a(n) = Sum_{i=floor((n-1)/2)..n-2} c(i+1), where c is the square characteristic (A010052).
%F A339184 a(n) = A339186(n) - A339183(n).
%e A339184 a(8) = 1; The partitions of 8 into 2 parts are (7,1), (6,2), (5,3) and (4,4). Since 4 is the only nonzero square appearing as a largest part, a(8) = 1.
%e A339184 a(9) = 0; The partitions of 9 into 2 parts are (8,1), (7,2), (6,3) and (5,4). Since there are no nonzero squares among the largest parts, a(9) = 0.
%t A339184 Table[Sum[Floor[Sqrt[n - i]] - Floor[Sqrt[n - i - 1]] , {i, Floor[n/2]}], {n, 0, 100}]
%Y A339184 Cf. A010052, A339183 (smaller part is a nonzero square), A339186 (total nonzero squares).
%K A339184 nonn,easy
%O A339184 0,18
%A A339184 _Wesley Ivan Hurt_, Nov 26 2020